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In this paper, we introduce a new approach for nonlinear equalization based on Gaussian processes for classification (GPC). We propose to measure the performance of this equalizer after a low-density parity-check channel decoder has detected the received sequence. Typically, most channel equalizers concentrate on reducing the bit error rate, instead of providing accurate posterior probability estimates. We show that the accuracy of these estimates is essential for optimal performance of the channel decoder and that the error rate output by the equalizer might be irrelevant to understand the performance of the overall communication receiver. In this sense, GPC is a Bayesian nonlinear classification tool that provides accurate posterior probability estimates with short training sequences. In the experimental section, we compare the proposed GPC-based equalizer with state-of-the-art solutions to illustrate its improved performance.